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Tag Archives: nullstellensatz
Commutative Algebra 61
In this article, we will consider algebraic geometry in the projective space. Throughout this article, k denotes an algebraically closed field. Projective Space Definition. Let . On the set , we consider the equivalence relation: The projective nspace is the set … Continue reading
Posted in Advanced Algebra
Tagged algebraic geometry, closed subsets, cones, graded rings, nullstellensatz, projective varieties, varieties
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Commutative Algebra 42
Noether Normalization Theorem Throughout this article, k is a field, not necessarily algebraically closed. Definition. Let A be a finitely generated kalgebra which is an integral domain. We say are algebraically independent over k if they are so as elements … Continue reading
Commutative Algebra 3
Algebraic Geometry Concepts We have decided to introduce, at this early point, some basics of algebraic geometry in order to motivate the later concepts. In summary, algebraic geometry studies solutions to polynomial equations over a field. First we consider a … Continue reading
Posted in Advanced Algebra
Tagged algebraic geometry, commutative rings, ideals, nullstellensatz, radical ideals, rings, topology, zariski topology
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